Some results in the theory of Orlicz spaces and applications to variational problems
Borderline sharp estimates for solutions to Neumann problems.
Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems
Local boundedness of minimizers of anisotropic functionals
Optimal Orlicz-Sobolev embeddings.
Optimal integrability of the Jacobian of orientation preserving maps
Dato un qualsiasi spazio invariante per riordinamenti su un insieme aperto , si determina il più piccolo spazio invariante per riordinamenti con la proprietà che se è una applicazione che mantiene l'orientamento e , allora appartiene localmente a .
Eigenfunctions of the Laplace-Beltrami Operator, and Isoperimetric and Isocapacitary Inequalities
Hardy inequalities with non-standard remainder terms
An optimal endpoint trace embedding
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
A sharp iteration principle for higher-order Sobolev embeddings
We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order involving...
Gradient regularity via rearrangements for -Laplacian type elliptic boundary value problems
A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.
The sharp Sobolev inequality in quantitative form
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